Ponder This — May’s Challenge!

ThinkPonder This Challenge:

Three people are playing the following betting game.

Every five minutes, a turn takes place in which a random player rests and the other two bet against one another with all of their money. The player with the smaller amount of money always wins, doubling his money by taking it from the loser.

For example, if the initial amounts of money are 1, 4, and 6, then the result of the first turn can be either 2,3,6 (1 wins against 4); 1,8,2 (4 wins against 6); or 2,4,5 (1 wins against 6). If two players with the same amount of money play against one another, the game immediately ends for all three players.

Your task is to find initial amounts of money for the three players, where none of the three has more than 255, and in such a way that the game cannot end in less than one hour.

In the example above (1,4,6), there is no way to end the game in less than 15 minutes.

Update (05/05): all three numbers should be positive integers. For example, [0,1,2], is not a valid answer since the game would end immediately.

IBM Research will post the names of those who submit a correct, original solution to their website! If you don’t want your name posted then please include such a statement in your submission!

We invite you to send your submission to the webmaster.

If you have any problems you think we might enjoy, please send them in. All replies should be sent to: webmster@us.ibm.com

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